Taliban officials told several usa media outlets on Saturday that they have held face-to-face meetings with American diplomats in Doha last week.
The Taliban source described as "useful" a meeting with Alice Wells, America's top diplomat for South Asia, last week. However, an important condition of Taliban for peace, in the words of one member of the delegation was the absence of representatives of the government of Afghanistan in further negotiations.
The Islamist insurgency had long called for direct talks with Washington.
"Any negotiations over the political future of Afghanistan will be between the Taliban and Afghan government", State Department spokeswoman Stephanie Newman told CNN.
Reports of Monday's landmark meeting in the Qatari capital appeared in American newspapers earlier this week but neither US officials nor the Taliban directly commented on them until now.
It wasn't clear when the next meeting would be held or with whom, but he was certain one would be held.
A senior representative of the Taliban said that the leaders of the movement for the first time held direct talks with USA officials.
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No comment from U.S. They added that there were "very positive signals" from the meeting, and that it was held in a "friendly atmosphere".
A former Taliban minister and ex-head of their political committee, Aga Jan Mohtism, who has maintained close contacts with the insurgent group, also confirmed a meeting in Doha took place earlier this week.
They also say they want a time frame for the withdrawal of the roughly 15,000 US and North Atlantic Treaty Organisation troops still in Afghanistan. According to the Mail Online, the Taliban are seeking a time frame for the withdrawal of some 15,000 USA and North Atlantic Treaty Organisation troops still in Afghanistan.
Not all of the roughly 14,000 United States troops now in Afghanistan have pulled back to cities.
Until now, Afghan President Ashraf Ghani's national security team said it is ready to hold talks with the Taleban at any time and that their allies, including the USA, should participate only as observers.
In Kabul, the Afghanistan President's office, ARG, on Saturday welcomed any support for peace efforts. Other unidentified United States diplomats were also present, according to two Taliban officials.
The New York Times reports that Trump's State Department is negotiating directly with the Taliban, with no involvement by Afghanistan's government.